Does model misspecification matter for hedging? A computational finance experiment based approach

To assess whether the model misspecification matters for hedging accuracy, we carefully select six increasingly complicated asset models, i.e., the Black–Scholes (BS) model, the Merton (M) model, the Heston (H) model, the Heston jump-diffusion (HJ) model, the double Heston (dbH) model and the double Heston jump-diffusion (dbHJ) model, and then impartially evaluate their performances in mitigating the risk of an option, under a controllable experimental market. In experiments, the ℙ measure asset paths are piecewisely simulated by a hybrid-model (including the Black–Scholes-type and the (double) Heston-type, with or without jump-diffusion term) with randomly given properly defined parameters. We access the hedging accuracy of six models within the operational dynamic hedging framework proposed by sun (2015), and apply the Fourier-COS-expansion method (i.e., the COS formula, Fang and Oosterlee (2008) to price options and to calculate the Greeks). Extensive numerical results indicate that the model misspecification shows no significant impact on hedging accuracy, but the market fit does matter critically for hedging.